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Probabilistic data association: the orbit set

Probabilistic data association: the orbit set
Probabilistic data association: the orbit set

This paper presents a novel method to obtain the solution to the initial orbit determination problem for optical observations as a continuum of orbits—namely the orbit set—that fits the set of acquired observations within a prescribed accuracy. Differential algebra is exploited to analytically link the uncertainty in the observations to the state of the orbiting body with truncated power series, thus allowing for a compact analytical description of the orbit set. The automatic domain splitting tool controls the truncation error of the polynomial approximation by patching the uncertainty domain with different polynomial expansions, effectively creating a mesh. The algorithm is tested for different observing strategies to understand the working boundaries, thus defining the region for which the admissible region is necessary to extract meaningful information from observations and highlight where the new method can achieve a smaller uncertainty region, effectively showing that for some observing strategies it is possible to extract more information from a tracklet than the attributable. Consequently, the method enables comparison of orbit sets avoiding sampling when looking for correlation of different observations. Linear regression is also implemented to improve the uncertainty estimation and study the influence of the confidence level on the orbit set size. This is shown both for simulated and real observations obtained from the TFRM observatory.

Differential algebra, High-order methods, Initial orbit determination, Space debris, Statistical analysis
0923-2958
Pirovano, Laura
1a69a10d-5e32-4a62-9e35-65e7154d5c2d
Santeramo, Daniele A.
2899e16a-da17-45b5-9869-3b762ac5310d
Armellin, Roberto
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Di Lizia, Pierluigi
8a0d7c21-8869-498e-95c8-41a8c8a6dd1a
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201
Pirovano, Laura
1a69a10d-5e32-4a62-9e35-65e7154d5c2d
Santeramo, Daniele A.
2899e16a-da17-45b5-9869-3b762ac5310d
Armellin, Roberto
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Di Lizia, Pierluigi
8a0d7c21-8869-498e-95c8-41a8c8a6dd1a
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201

Pirovano, Laura, Santeramo, Daniele A., Armellin, Roberto, Di Lizia, Pierluigi and Wittig, Alexander (2020) Probabilistic data association: the orbit set. Celestial Mechanics and Dynamical Astronomy, 132 (2), [15]. (doi:10.1007/s10569-020-9951-z).

Record type: Article

Abstract

This paper presents a novel method to obtain the solution to the initial orbit determination problem for optical observations as a continuum of orbits—namely the orbit set—that fits the set of acquired observations within a prescribed accuracy. Differential algebra is exploited to analytically link the uncertainty in the observations to the state of the orbiting body with truncated power series, thus allowing for a compact analytical description of the orbit set. The automatic domain splitting tool controls the truncation error of the polynomial approximation by patching the uncertainty domain with different polynomial expansions, effectively creating a mesh. The algorithm is tested for different observing strategies to understand the working boundaries, thus defining the region for which the admissible region is necessary to extract meaningful information from observations and highlight where the new method can achieve a smaller uncertainty region, effectively showing that for some observing strategies it is possible to extract more information from a tracklet than the attributable. Consequently, the method enables comparison of orbit sets avoiding sampling when looking for correlation of different observations. Linear regression is also implemented to improve the uncertainty estimation and study the influence of the confidence level on the orbit set size. This is shown both for simulated and real observations obtained from the TFRM observatory.

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More information

Published date: 23 February 2020
Additional Information: Funding Information: The work presented was partially supported by EOARD under Grant FA9550-15-1-0244 and Surrey Space Centre (SSC). The authors want to thank Dr. Gennaro Principe who provided the codes for the AD algorithm. The authors also acknowledge the anonymous reviewers for the valuable comments. Publisher Copyright: © 2020, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
Keywords: Differential algebra, High-order methods, Initial orbit determination, Space debris, Statistical analysis

Identifiers

Local EPrints ID: 446841
URI: http://eprints.soton.ac.uk/id/eprint/446841
ISSN: 0923-2958
PURE UUID: c748e773-7252-4976-bea8-eac781656c9a
ORCID for Alexander Wittig: ORCID iD orcid.org/0000-0002-4594-0368

Catalogue record

Date deposited: 24 Feb 2021 17:31
Last modified: 25 Feb 2021 02:50

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Contributors

Author: Laura Pirovano
Author: Daniele A. Santeramo
Author: Pierluigi Di Lizia
Author: Alexander Wittig ORCID iD

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